Advances in Multifield Theories for Continua with Substructure
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Beschreibung
The current use of complex materials in nanotechnology and industrial engineering has led to a number of intricate problems in mechanics. The macroscopic behavior of such materials often depends critically on their substructures. Multifield theories in continuum mechanics provide the tools for modeling and describing these material substructures, as is emphasized in this book. Indeed multifield theories are an active area of research because of the numerous theoretical and numerical problems emerging in the field.
Written by leading mathematicians and engineers, the chapters feature a broad range of topics that offer both experimental results and clear, detailed answers to fundamental questions about the general formulation of multifield theories. Amid a rich collection of open problems, selected subjects treated include:
* Energetic and geometric properties of elastic-plastic materials
* Poisson structures for complex fluids
* Drag reduction in turbulence due to polymeric substructures
* Topological properties of stresses and defects
* Exact relations for the effective behavior of composites
* Multifield macroscopic modeling of shape memory effects and extended thermodynamics
* Properties of junctions and interfaces
Applied mathematicians, mechanical and structural engineers, material scientists, graduate students, and researchers in the above areas will benefit from this work.
Contributors:
D. Bernardini, G. Capriz, C. M. Casciola, H. Cendra, E. DeAngelis, Y. Grabovsky, P. M. Mariano, J. Marsden, I. Müller, O. B. Naimark, G. Parry, T. J. Pence, R. Piva, T. S. Ratiu, R. Segev, M. Silhavy
Toachieve design, implementation,and servicing ofcomplex systems and struc tures in an efficient and cost-effective way,a deeper knowledge and understanding of the subtle cast and detailed evolution of materials is needed. The analysis in demand borders with the molecular and atomic one, spanning all the way down from classical continua. The study of the behavior of complex materials in sophisticated devices also opens intricate questions about the applicability of primary axioms ofcontinuum mechanics such as the ultimate nature of the material element itselfand the possibility ofidentifying itperfectly. So it is necessary to develop tools that allow usto formulate both theoretical models and methods of numerical approximation for the analysis of material substructures. Multifield theories in continuum mechanics, which bridge classical materials science and modern continuum mechanics, provide precisely these tools. Multifield theories not only address problems of material substructures, but also encompass well-recognized approaches to the study of soft condensed matter and allow one to model disparate conditions in various states ofmatter. However, research inmultifield theories is vast, and there is little in the way of a comprehensive distillation of the subject from an engineer's perspective. Therefore, the papers in the present volume, 1 which grew out of our experience as editors for an engineeringjournal, tackle some fundamental questions,suggest solutions of concrete problems, and strive to interpret a host of experimental evidence. In this spirit, each of the authors has contributed original results having in mind their wider applicability.
Energetic and geometric properties of elastic-plastic materials Poisson structures for complex fluids Drag reduction in turbulence due to polymeric substructures Topological properties of stresses and defects Exact relations for the effective behavior of composites Multifield macroscopic modeling of shape memory effects and extended thermodynamics Properties of junctions and interfaces
The current use of complex materials in nanotechnology and industrial engineering has led to a number of intricate problems in mechanics, and the macroscopic behavior of such materials often depends critically on their substructures. This work, written by leading mathematicians and engineers, features a broad range of topics that offer both experimental results and clear, detailed answers to fundamental questions about the general formulation of multifield theories within the context of modeling material substructures. Applied mathematicians, mechanical and structural engineers, material scientists, graduate students, and researchers in the above areas will benefit from the work and may find suggestions for further research in its rich collection of open problems.
Autor*in
Gianfranco Capriz
Themen in »Advances in Multifield Theories for Continua with Substructure«
Algebra composite continuum mechanics dynamics geometry mechanics modeling plasticity stress thermodynamics transitions
Stimmen zu »Advances in Multifield Theories for Continua with Substructure«
"As an outgrowth of a symposium held in Taormina, Italy, in 2001, ten invited papers on multifield theories for continua with substructure are presented here. Multifield theories aim to bridge the area between materials science and continuum mechanics. From the standpoint of material constituents, the simplest model is considered in the contribution of I. Müller: a monatomic gas.… Other contributions deal with the interaction of polymer chains and the turbulent state of a fluid…with topological properties of defects, of shape memory and others. The perhaps most theoretical article is by Cendra, Marsden and Ratiu on…extended…Poisson brackets with cocycles. The articles, though dealing with nontrivial matters, are quite readable and informative even for the nonspecialist."
—Monatshefte für Mathematik
"...This compendium is extremely diverse ...The individual contributions in this compendium are certainly quite interesting and worth reading."
—Rezensionen
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